* The following were written up as revision during my mid-semester break, with some corners cut and proofs added where needed. I've skipped the first couple of chapters because they're boring and largely irrelevant.* # Cauchy Sequences Our motivation for defining and investigating Cauchy … [Read more...]
Network Theory | Preface and Chapter 1
*The following notes are from "A First Course in Network Theory", by Estrada and Knight".* #Preface - Originated from lecture notes - Difficult to balance theory and application, catering to a highly diverse student cluster (in lectures_ - Avoid heavy math bias *(dammit)* - No … [Read more...]
Griffith’s QM | The Wave Function
#The Schrodinger Equation Consider a particle constrained on the x-axis, with mass $m$, subjected to a force $F(x,t)$. - In Classical mechanics, we determined $x(t)$, the position. Then we find $v = \frac{dx}{dt}$ the velocity, and momentum $p = mv$. Finally, we determine the kinetic energy $T … [Read more...]
Griffith’s Quantum Mechanics | Preface
- QM was not created by one individual, and retains 'scars' from its traumatic youth. >'I think I can safely say that nobody understands quantum mechanics.' -Feynman - One cannot understand what quantum mechanics *means* until one understands what it *does*. That's what this book is … [Read more...]
Notes: Spivak’s Calculus Prologue C1 Inequalities
**Note: I lost a page from my notepad, so this is not a continuous stream of notes in that if we let $\epsilon … [Read more...]
Notes: Spivak’s Calculus Preface and Prologue Chapter 1
- Book is driven by a 'desire to present calculus not as a prelude, but a first real encounter with mathematics'. - Precision and rigour shouldn't be deterrents - they are the natural medium for formulating mathematical questions - 29 Chapters, with 2 'starred' as optional - Presented as an … [Read more...]
Next Gen Infrastructures Module 1
# Module 1: Complexity and Infrastructures # Grand challenge: An infrastructure meeting twice the needs of today's population, with half the resources, providing twice the livability. Complexity of infrastructures causes emergent issues. - examples - Multifunctionality in infrastructures - … [Read more...]